Finite Group Databasebeta

← #29573556

Subgroups — #29573556

Order 15616.

530 conjugacy classes of subgroups; only the 123 normal subgroups are shown.

normal subgroups only

This group has 530 conjugacy classes of subgroups — too many to draw. Only its 123 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#21448729C211yesmaximal, characteristic
2#21444137C211yesmaximal, characteristic
3#21443697C212yesmaximal, complemented
4#21443686C212yesmaximal, complemented
5C61×#1799C211yesmaximal, characteristic
6C2×D4×Dic61—21no—
7C2×C22⋊#92418C2212yes—
8#16839661—21no—
9#16839637—21no—
10#16839637—21no—
11#16839628C411yescharacteristic, complemented
12#16839622C411yescharacteristic, complemented
13#16839622C2211yescharacteristic
14C4×C4⋊Dic61C411yescharacteristic, complemented
15C2×#14519684C411yescharacteristic, complemented
16C2×#14519684C2211yescharacteristic
17#16839488—21no—
18#16839486—21no—
19C2×C4×D4×C61C2211yescharacteristic
20C2×#99×C61—21no—
21C61×#380C2212yes—
22C61×#342—21no—
23C23×Dic61—21no—
24C23×Dic61—21no—
25C22×#92418—22no—
26D4×Dic61—42no—
27D4×Dic61—42no—
28C2×C4⋊Dic61—21no—
29C2×C4⋊Dic61—21no—
30C2×C4⋊Dic61—21no—
31C2×C4⋊Dic61—21no—
32C2×C22⋊Dic61—21no—
33C2×C22⋊Dic61—21no—
34C2×C4×Dic61—21no—
35C22⋊#92418—22no—
36C22⋊#92418—22no—
37#14519684—21no—
38#14519684—21no—
39#14519684—21no—
40#14519684C2×C411yescharacteristic
41#14519684C2×C411yescharacteristic
42#14519684C2×C411yescharacteristic
43#14519684C2×C411yescharacteristic
44C22×D4×C61D411yescharacteristic
45C23×C4×C61C2×C411yescharacteristic
46C23×C4×C61C2311yescharacteristic
47C4×D4×C61—22no—
48C4×D4×C61—22no—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61D411yescharacteristic
51C2×C22⋊C4×C61—22no—
52C2×C22⋊C4×C61D411yescharacteristic
53C2×C22⋊C4×C61D411yescharacteristic
54C2×C42×C61C2×C411yescharacteristic
55#99×C61—42no—
56#95×C61—22no—
57C24×C61C22⋊C411yescharacteristic
58C24×C61C2×D411yescharacteristic
59C2×D4×C61—22no—
60C2×D4×C61—22no—
61C2×D4×C61D812yes—
62C2×D4×C61SD1612yes—
63C22×C4×C61—21no—
64C22×C4×C61—21no—
65C22×C4×C61—42no—
66C22×C4×C61—81no—
67C22×C4×C61—81no—
68C22×C4×C61C22⋊C411yescharacteristic
69C22×C4×C61C22⋊C411yescharacteristic
70C22×C4×C61C22⋊C411yescharacteristic
71C22×C4×C61C22×C411yescharacteristic
72C22×C4×C61C2×D411yescharacteristic
73C22×C4×C61#4112yes—
74C22×C4×C61#4112yes—
75C22×Dic61—21no—
76C22×Dic61—21no—
77C22×Dic61—21no—
78C22×Dic61—21no—
79C22×Dic61—42no—
80C22×Dic61—42no—
81C22×Dic61—42no—
82C22×Dic61—41no—
83C22×Dic61—41no—
84C22×Dic61—81no—
85C22×Dic61—81no—
86C4⋊C4×C61—22no—
87C4⋊C4×C61—82no—
88C22⋊C4×C61—22no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—42no—
91C22⋊C4×C61—42no—
92C42×C61—21no—
93C42×C61—21no—
94C22⋊Dic61—42no—
95C22⋊Dic61—41no—
96C22⋊Dic61—41no—
97C4⋊Dic61—42no—
98C4⋊Dic61—42no—
99C4⋊Dic61—81no—
100C4⋊Dic61—81no—
101C4×Dic61—42no—
102C2×#92418—42no—
103C2×#92418—82no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61—41no—
107C23×C61—41no—
108C23×C61—41no—
109C23×C61—41no—
110C23×C61#10212yes—
111C23×C61C2×C22⋊C411yescharacteristic
112C23×C61#12312yes—
113C23×C61C2×D811yescharacteristic
114C23×C61C2×SD1611yescharacteristic
115C23×C61#13712yes—
116D4×C61—24no—
117D4×C61—24no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—42no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—41no—
126C2×C4×C61—41no—
127C2×C4×C61—41no—
128C2×C4×C61—81no—
129C2×C4×C61—81no—
130C2×C4×C61—82no—
131C2×C4×C61—82no—
132C2×C4×C61—82no—
133C2×C4×C61#10212yes—
134C2×C4×C61#11711yescharacteristic
135C2×C4×C61#11711yescharacteristic
136C2×C4×C61#12312yes—
137C2×Dic61—22no—
138C2×Dic61—41no—
139C2×Dic61—41no—
140C2×Dic61—41no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—41no—
144C2×Dic61—41no—
145C2×Dic61—41no—
146C2×Dic61—41no—
147C2×Dic61—41no—
148C2×Dic61—41no—
149C2×Dic61—82no—
150C2×Dic61—82no—
151C2×Dic61—84no—
152#92418—82no—
153#8760—611nomaximal, Sylow
154C22×C61—21no—
155C22×C61—22no—
156C22×C61—21no—
157C22×C61—22no—
158C22×C61—22no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61—42no—
162C22×C61—42no—
163C22×C61—42no—
164C22×C61—41no—
165C22×C61—41no—
166C22×C61#38111yescharacteristic
167C22×C61C2×#10211yescharacteristic
168C22×C61#41911yescharacteristic
169C22×C61#48012yes—
170C22×C61#48312yes—
171C4×C61—22no—
172C4×C61—22no—
173C4×C61—21no—
174C4×C61—21no—
175C4×C61—41no—
176C4×C61—41no—
177C4×C61—162no—
178Dic61—42no—
179Dic61—81no—
180Dic61—81no—
181Dic61—81no—
182#2349—611no—
183#1799D6111yescharacteristic
184#1459—611no—
185#1294—612no—
186#1289—612no—
187C2×C61—21no—
188C2×C61—22no—
189C2×C61—21no—
190C2×C61—22no—
191C2×C61—42no—
192C2×C61#182311yescharacteristic
193C2×C61#182711yescharacteristic
194C2×C61#182811yescharacteristic
195C2×C4×D4—1221no—
196C2×C4×D4C2×D6111yescharacteristic
197C2×#99—21no—
198C2×C22⋊C8—612no—
199#389—1221no—
200#385—1221no—
201#385—1221no—
202#382—611no—
203#380—611no—
204#380—611no—
205#380C2×D6112yes—
206C4×C4⋊C4—611no—
207C2×#95—611no—
208C2×#95—611no—
209#342—21no—
210#324—1221no—
211#323—1221no—
212C61#876011yescharacteristic, complemented, Sylow
213C22×D4C22⋊D6111yescharacteristic
214C23×C4—1221no—
215C23×C4—1221no—
216C23×C4C4×D6111yescharacteristic
217C23×C4C22×D6111yescharacteristic
218C22×C8—1222no—
219C4×D4—22no—
220C4×D4—22no—
221C4×D4—2442no—
222C4×D4—2442no—
223C2×C4⋊C4—22no—
224C2×C4⋊C4—1221no—
225C2×C4⋊C4—1221no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4D24411yescharacteristic
229C2×C22⋊C4—22no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C22⋊C4D24411yescharacteristic
233C2×C22⋊C4C22⋊D6111yescharacteristic
234C2×C42—1221no—
235C2×C42C4×D6111yescharacteristic
236#99—42no—
237C22⋊C8—1222no—
238C22⋊C8—1222no—
239#95—22no—
240#95—611no—
241#95—611no—
242#95—611no—
243#95—611no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247C24#1175819811yescharacteristic
248C24C2×C22⋊D6111yescharacteristic
249C2×D4—22no—
250C2×D4—22no—
251C2×D4#1175819912yes—
252C2×D4#1175820112yes—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—42no—
256C22×C4—81no—
257C22×C4—81no—
258C22×C4—1221no—
259C22×C4—1221no—
260C22×C4—1221no—
261C22×C4—1221no—
262C22×C4—4881no—
263C22×C4—4881no—
264C22×C4—2442no—
265C22×C4—2442no—
266C22×C4—2442no—
267C22×C4—2441no—
268C22×C4—2441no—
269C22×C4#1175819811yescharacteristic
270C22×C4#1175819811yescharacteristic
271C22×C4#1175819811yescharacteristic
272C22×C4C2×C4×D6111yescharacteristic
273C22×C4C2×D24411yescharacteristic
274C22×C4#1175822412yes—
275C22×C4#1175822412yes—
276C2×C8—4882no—
277C2×C8—2442no—
278C4⋊C4—22no—
279C4⋊C4—82no—
280C4⋊C4—4881no—
281C4⋊C4—4881no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C22⋊C4—22no—
285C22⋊C4—22no—
286C22⋊C4—42no—
287C22⋊C4—42no—
288C22⋊C4—2442no—
289C22⋊C4—2441no—
290C22⋊C4—2441no—
291C42—21no—
292C42—21no—
293C42—2442no—
294C23—21no—
295C23—21no—
296C23—41no—
297C23—41no—
298C23—41no—
299C23—41no—
300C23#1451969712yes—
301C23C2×#1175819811yescharacteristic
302C23#1451975812yes—
303C23C2×#1175819911yescharacteristic
304C23C2×#1175820111yescharacteristic
305C23#1451980712yes—
306D4—24no—
307D4—24no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—41no—
314C2×C4—42no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—81no—
319C2×C4—81no—
320C2×C4—82no—
321C2×C4—82no—
322C2×C4—82no—
323C2×C4—1222no—
324C2×C4—4882no—
325C2×C4—4882no—
326C2×C4—4884no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2441no—
332C2×C4—2441no—
333C2×C4—2441no—
334C2×C4—2441no—
335C2×C4—2441no—
336C2×C4—2441no—
337C2×C4—2441no—
338C2×C4#1451969712yes—
339C2×C4#1451973311yescharacteristic
340C2×C4#1451973311yescharacteristic
341C2×C4#1451976112yes—
342C8—4882no—
343C22—21no—
344C22—22no—
345C22—21no—
346C22—22no—
347C22—22no—
348C22—41no—
349C22—41no—
350C22—42no—
351C22—42no—
352C22—42no—
353C22—41no—
354C22—41no—
355C22#1683962311yescharacteristic
356C22C2×#1451969711yescharacteristic
357C22#1683977011yescharacteristic
358C22#1684007312yes—
359C22#1684009012yes—
360C4—22no—
361C4—22no—
362C4—21no—
363C4—21no—
364C4—41no—
365C4—41no—
366C4—162no—
367C4—4881no—
368C4—4881no—
369C4—4881no—
370C4—2442no—
371C2—22no—
372C2—21no—
373C2—21no—
374C2—22no—
375C2—42no—
376C2#2144590311yescharacteristic
377C2#2144592011yescharacteristic
378C2#2144592511yescharacteristic
subgroupG/H
centerC22#16839623
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC61×#1799C2
socleC22×C61#381
prime radicalC22×D4×C61D4
cosocleC23×C4×C61C23
hypercenter#1799D61
hypocenterC61#8760
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1799

Complements

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

NH ≅ G/Ntype
3. #21443697C2semidirect
4. #21443686C2semidirect
11. #16839628C4semidirect
12. #16839622C4semidirect
14. C4×C4⋊Dic61C4semidirect
15. C2×#14519684C4semidirect
212. C61#8760semidirect

Maximal subgroups

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

subgroupindex
#214487292
#214441372
#214436972
#214436862
C61×#17992
#876061