Finite Group Databasebeta

← #29575793

Subgroups — #29575793

Order 15616.

692 conjugacy classes of subgroups; only the 147 normal subgroups are shown.

normal subgroups only

This group has 692 conjugacy classes of subgroups — too many to draw. Only its 147 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#21454150C211yesmaximal, characteristic
2#21445887C211yesmaximal, characteristic, complemented
3C2×#16839495C212yesmaximal
4#21443698C212yesmaximal, complemented
5C2×C61×#382C211yesmaximal, characteristic, complemented
6C2×#14519760—21no—
7C2×#14519751C2211yescharacteristic
8C2×C22⋊#92418C2212yes—
9#16839664C412yescomplemented
10#16839660C412yescomplemented
11#16839653—22no—
12#16839641—21no—
13#16839622C2211yescharacteristic
14#16839517—22no—
15#16839495—24no—
16C22×C4⋊C4×C61—21no—
17C22×C42×C61C2211yescharacteristic
18C61×#382—24no—
19C2×#95×C61—21no—
20C2×#95×C61C2212yes—
21C22×D244C2×C411yescharacteristic
22C22×C22⋊D61—21no—
23C22×#92418—22no—
24#14519760—42no—
25#14519760—42no—
26#14519751—22no—
27#14519751—22no—
28C2×C4⋊Dic61C2×C411yescharacteristic
29C2×C4⋊Dic61C2×C412yes—
30C2×#11758196—22no—
31C2×C22⋊Dic61—21no—
32C2×#11758198—22no—
33C2×#11758198—22no—
34C2×#11758198—21no—
35C22⋊#92418—22no—
36C22⋊#92418—22no—
37#14519684—22no—
38#14519684—21no—
39C23×C4×C61—22no—
40C23×C4×C61D411yescharacteristic
41C23×C4×C61D411yescharacteristic
42C23×C4×C61C2311yescharacteristic
43C2×C4⋊C4×C61—24no—
44C2×C4⋊C4×C61—42no—
45C2×C4⋊C4×C61—42no—
46C2×C42×C61—22no—
47C2×C42×C61—22no—
48C2×C42×C61C2×C412yes—
49C2×C42×C61D412yes—
50#95×C61—24no—
51#95×C61—22no—
52#95×C61D414yes—
53C24×C61C2×D411yescharacteristic
54C23×D61—21no—
55C22×C4×C61—21no—
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—24no—
62C22×C4×C61—42no—
63C22×C4×C61—42no—
64C22×C4×C61—44no—
65C22×C4×C61—44no—
66C22×C4×C61—42no—
67C22×C4×C61—42no—
68C22×C4×C61C22⋊C412yes—
69C22×C4×C61C22⋊C412yes—
70C22×C4×C61D812yes—
71C22×C4×C61SD1612yes—
72C22×C4×C61C22×C411yescharacteristic
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×D412yes—
75C22×C4×C61#4112yes—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C2×C22⋊D61—41no—
80C2×C22⋊D61—41no—
81C2×C22⋊D61—41no—
82C22×Dic61—21no—
83C22×Dic61—22no—
84C2×D244—22no—
85C2×D244—42no—
86C4⋊C4×C61—48no—
87C42×C61—24no—
88C42×C61—24no—
89C22⋊Dic61—41no—
90C22⋊Dic61—41no—
91#11758198—44no—
92#11758198—44no—
93#11758198—42no—
94C4⋊Dic61—22no—
95C4⋊Dic61—42no—
96#11758196—44no—
97C2×#92418—44no—
98C2×#92418—42no—
99C23×C61—22no—
100C23×C61—22no—
101C23×C61C2×C22⋊C411yescharacteristic
102C23×C61#12011yescharacteristic
103C23×C61#12311yescharacteristic
104C23×C61C2×D811yescharacteristic
105C23×C61C2×SD1611yescharacteristic
106C23×C61AGL(1,ℤ/8)11yescharacteristic
107C23×C61#13711yescharacteristic
108C22×D61—41no—
109C22×D61—42no—
110C22×D61—41no—
111C22×D61—41no—
112C22×D61—42no—
113C2×C4×C61—22no—
114C2×C4×C61—22no—
115C2×C4×C61—22no—
116C2×C4×C61—22no—
117C2×C4×C61—22no—
118C2×C4×C61—22no—
119C2×C4×C61—22no—
120C2×C4×C61—22no—
121C2×C4×C61—22no—
122C2×C4×C61—22no—
123C2×C4×C61—22no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—42no—
127C2×C4×C61—42no—
128C2×C4×C61—44no—
129C2×C4×C61—44no—
130C2×C4×C61—44no—
131C2×C4×C61—84no—
132C2×C4×C61—84no—
133C2×C4×C61#10214yes—
134C2×C4×C61C4×D412yes—
135C2×C4×C61#12112yes—
136C22⋊D61—81no—
137C22⋊D61—81no—
138C22⋊D61—81no—
139C22⋊D61—81no—
140C2×Dic61—41no—
141C2×Dic61—42no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—42no—
146D244—82no—
147#92418—82no—
148#9156—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61#38611yescharacteristic
158C22×C61#41012yes—
159C22×C61C2×#10211yescharacteristic
160C22×C61#41711yescharacteristic
161C22×C61#42112yes—
162C22×C61#44711yescharacteristic
163C22×C61#44811yescharacteristic
164C22×C61#48011yescharacteristic
165C22×C61#48111yescharacteristic
166C2×D61—81no—
167C2×D61—81no—
168C2×D61—81no—
169C2×D61—82no—
170C2×D61—82no—
171C4×C61—24no—
172C4×C61—22no—
173C4×C61—22no—
174C4×C61—42no—
175C4×C61—84no—
176Dic61—81no—
177Dic61—82no—
178#2854—611no—
179C2×#382D6111yescharacteristic, complemented
180#1817—611no—
181C2×#327—612no—
182#1294—612no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61#151212yes—
188C2×C61#151712yes—
189C2×C61#187411yescharacteristic
190C2×C61#189711yescharacteristic
191C2×C61#189911yescharacteristic
192D61—161no—
193C2×#123—1221no—
194C2×#121—611no—
195C22×C4⋊C4—21no—
196C22×C42C2×D6111yescharacteristic
197C2×C22⋊C8—612no—
198#390—612no—
199#389—612no—
200#388—1222no—
201#386—1221no—
202#382—24no—
203#380—611no—
204C2×#95—21no—
205C2×#95C2×D6112yes—
206#336—1222no—
207#327—1224no—
208C61#915611yescharacteristic, complemented, Sylow
209C22×D4—611no—
210C22×D4—1221no—
211C23×C4—22no—
212C23×C4C22⋊D6111yescharacteristic
213C23×C4C22⋊D6111yescharacteristic
214C23×C4C22×D6111yescharacteristic
215C22×C8—1222no—
216#123—2442no—
217#123—2442no—
218#121—1222no—
219#121—1222no—
220C2×C4⋊C4—24no—
221C2×C4⋊C4—42no—
222C2×C4⋊C4—42no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—612no—
225C2×C4⋊C4—1222no—
226C2×C22⋊C4—1221no—
227C2×C22⋊C4—1222no—
228C2×C22⋊C4—1222no—
229C2×C22⋊C4—1221no—
230C2×C42—22no—
231C2×C42—22no—
232C2×C42C4×D6112yes—
233C2×C42D24412yes—
234C22⋊C8—1222no—
235C22⋊C8—1222no—
236#95—24no—
237#95—22no—
238#95—1222no—
239#95—1221no—
240#95C22⋊D6114yes—
241C24—1221no—
242C24C2×C22⋊D6111yescharacteristic
243C2×D4—1222no—
244C2×D4—2442no—
245C2×D4—2441no—
246C2×D4—2441no—
247C2×D4—2441no—
248C2×D4—2441no—
249C2×D4—2441no—
250C2×D4—2441no—
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—24no—
258C22×C4—42no—
259C22×C4—42no—
260C22×C4—44no—
261C22×C4—44no—
262C22×C4—42no—
263C22×C4—42no—
264C22×C4—1222no—
265C22×C4—1221no—
266C22×C4#1175819812yes—
267C22×C4#1175819812yes—
268C22×C4#1175819912yes—
269C22×C4#1175820112yes—
270C22×C4C2×C4×D6111yescharacteristic
271C22×C4C2×D24411yescharacteristic
272C22×C4#1175822212yes—
273C22×C4C2×C22⋊D6112yes—
274C2×C8—2444no—
275C2×C8—2442no—
276C4⋊C4—48no—
277C4⋊C4—1222no—
278C4⋊C4—2442no—
279C4⋊C4—2444no—
280C22⋊C4—2444no—
281C22⋊C4—2441no—
282C22⋊C4—2441no—
283C22⋊C4—2444no—
284C22⋊C4—2442no—
285C42—24no—
286C42—24no—
287C23—22no—
288C23—22no—
289C23—2442no—
290C23—2441no—
291C23—2441no—
292C23—2442no—
293C23—2441no—
294C23C2×#1175819811yescharacteristic
295C23#1451974611yescharacteristic
296C23#1451976011yescharacteristic
297C23C2×#1175819911yescharacteristic
298C23C2×#1175820111yescharacteristic
299C23#1451980311yescharacteristic
300C23#1451980811yescharacteristic
301D4—4882no—
302D4—4881no—
303D4—4881no—
304D4—4881no—
305D4—4881no—
306C2×C4—22no—
307C2×C4—22no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—22no—
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—42no—
320C2×C4—42no—
321C2×C4—44no—
322C2×C4—44no—
323C2×C4—44no—
324C2×C4—84no—
325C2×C4—84no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2442no—
331C2×C4—2441no—
332C2×C4#1451969714yes—
333C2×C4C4×C22⋊D6112yes—
334C2×C4#1451975112yes—
335C8—4882no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—21no—
341C22—21no—
342C22—21no—
343C22—21no—
344C22—4882no—
345C22—4882no—
346C22—4881no—
347C22—4881no—
348C22—4881no—
349C22#1683964111yescharacteristic
350C22#1683973512yes—
351C22C2×#1451969711yescharacteristic
352C22#1683976111yescharacteristic
353C22#1683978012yes—
354C22#1683989611yescharacteristic
355C22#1683990111yescharacteristic
356C22#1684007511yescharacteristic
357C22#1684008011yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—84no—
363C4—4882no—
364C4—4881no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—9761no—
370C2#2144435512yes—
371C2#2144437812yes—
372C2#2144613611yescharacteristic
373C2#2144626711yescharacteristic
374C2#2144627711yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#382C2
socleC23×C61C2×C22⋊C4
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenterC2×#382D61
hypocenterC61#9156
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#382

Complements

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

NH ≅ G/Ntype
2. #21445887C2semidirect
4. #21443698C2semidirect
5. C2×C61×#382C2semidirect
9. #16839664C4semidirect
10. #16839660C4semidirect
179. C2×#382D61semidirect
208. C61#9156semidirect

Maximal subgroups

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

subgroupindex
#214541502
#214458872
C2×#168394952
#214436982
C2×C61×#3822
#915661