Finite Group Databasebeta

← #29576079

Subgroups — #29576079

Order 15616.

622 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 622 conjugacy classes of subgroups — too many to draw. Only its 127 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#21451561C211yesmaximal, characteristic
2#21448437C211yesmaximal, characteristic, complemented
3#21444388C212yesmaximal
4#21443687C212yesmaximal, complemented
5C2×C61×#324C211yesmaximal, characteristic, complemented
6C2×#14519760—21no—
7C2×#14519751C2211yescharacteristic
8C2×#14519736—21no—
9#16839692C412yescomplemented
10#16839684—22no—
11#16839679C412yescomplemented
12#16839661—24no—
13#16839641—21no—
14#16839622—21no—
15#16839622C2211yescharacteristic
16#16839622C2212yes—
17#16839497—24no—
18C22×C4⋊C4×C61C2211yescharacteristic
19C2×C22⋊C8×C61C2212yes—
20C61×#324—22no—
21C22×D244C2×C411yescharacteristic
22C22×C22⋊D61—21no—
23#14519760—42no—
24#14519760—42no—
25#14519751—22no—
26#14519751—22no—
27#14519736—42no—
28#14519736—42no—
29C2×C4⋊Dic61—22no—
30C2×C4⋊Dic61—22no—
31C2×C4⋊Dic61—21no—
32C2×C4⋊Dic61—22no—
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×#11758196—22no—
35C2×C22⋊Dic61—22no—
36C2×C22⋊Dic61—21no—
37C2×#11758198—22no—
38C2×#11758198—21no—
39C2×#11758198—22no—
40C2×C4×Dic61—22no—
41#14519684—22no—
42#14519684—22no—
43#14519684C2×C412yes—
44#14519684D414yes—
45C23×C4×C61D411yescharacteristic
46C23×C4×C61D411yescharacteristic
47C23×C4×C61C2311yescharacteristic
48C22×C8×C61—22no—
49C2×C4⋊C4×C61—22no—
50C2×C4⋊C4×C61—22no—
51C2×C4⋊C4×C61C2×C412yes—
52C2×C4⋊C4×C61D412yes—
53C22⋊C8×C61—22no—
54C22⋊C8×C61—22no—
55C24×C61C2×D411yescharacteristic
56C23×D61—21no—
57C22×C4×C61—21no—
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61—21no—
61C22×C4×C61—21no—
62C22×C4×C61—21no—
63C22×C4×C61—81no—
64C22×C4×C61—81no—
65C22×C4×C61C22⋊C412yes—
66C22×C4×C61C22⋊C412yes—
67C22×C4×C61D812yes—
68C22×C4×C61SD1612yes—
69C22×C4×C61C22×C411yescharacteristic
70C22×C4×C61C2×D412yes—
71C22×C4×C61C2×D411yescharacteristic
72C22×C4×C61#4112yes—
73C2×C22⋊D61—41no—
74C2×C22⋊D61—41no—
75C2×C22⋊D61—41no—
76C2×C22⋊D61—41no—
77C2×C22⋊D61—41no—
78C2×C22⋊D61—41no—
79C22×Dic61—21no—
80C22×Dic61—22no—
81C22×Dic61—24no—
82C2×D244—22no—
83C2×D244—81no—
84C2×C8×C61—42no—
85C2×C8×C61—82no—
86C4⋊C4×C61—24no—
87C4⋊C4×C61—24no—
88C22⋊Dic61—42no—
89C22⋊Dic61—41no—
90C22⋊Dic61—41no—
91C22⋊Dic61—42no—
92#11758198—44no—
93#11758198—42no—
94#11758198—82no—
95C4⋊Dic61—22no—
96C4⋊Dic61—44no—
97C4⋊Dic61—82no—
98C4⋊Dic61—82no—
99C4⋊Dic61—81no—
100#11758196—44no—
101C4×Dic61—44no—
102C23×C61—41no—
103C23×C61—41no—
104C23×C61C2×C22⋊C411yescharacteristic
105C23×C61#12011yescharacteristic
106C23×C61#12311yescharacteristic
107C23×C61C2×D811yescharacteristic
108C23×C61C2×SD1611yescharacteristic
109C23×C61AGL(1,ℤ/8)11yescharacteristic
110C23×C61#13711yescharacteristic
111C22×D61—42no—
112C22×D61—42no—
113C22×D61—41no—
114C22×D61—41no—
115C22×D61—41no—
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—41no—
124C2×C4×C61—42no—
125C2×C4×C61—42no—
126C2×C4×C61—41no—
127C2×C4×C61—42no—
128C2×C4×C61—42no—
129C2×C4×C61—81no—
130C2×C4×C61#10214yes—
131C2×C4×C61C4×D412yes—
132C2×C4×C61#12112yes—
133C22⋊D61—81no—
134C22⋊D61—81no—
135C22⋊D61—81no—
136C22⋊D61—81no—
137C2×Dic61—44no—
138C2×Dic61—42no—
139C2×Dic61—44no—
140C2×Dic61—42no—
141C2×Dic61—41no—
142C2×Dic61—41no—
143C2×Dic61—42no—
144C2×Dic61—41no—
145C2×Dic61—44no—
146D244—82no—
147C8×C61—82no—
148#9204—611nomaximal, Sylow
149C22×C61—21no—
150C22×C61—21no—
151C22×C61—21no—
152C22×C61—21no—
153C22×C61—21no—
154C22×C61—21no—
155C22×C61—41no—
156C22×C61—41no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61#38611yescharacteristic
160C22×C61C2×#10211yescharacteristic
161C22×C61#41711yescharacteristic
162C22×C61#44711yescharacteristic
163C22×C61#44811yescharacteristic
164C22×C61#48011yescharacteristic
165C22×C61#48111yescharacteristic
166C2×D61—82no—
167C2×D61—82no—
168C2×D61—81no—
169C2×D61—81no—
170C2×D61—81no—
171C4×C61—24no—
172C4×C61—22no—
173C4×C61—22no—
174C4×C61—42no—
175Dic61—84no—
176Dic61—82no—
177Dic61—81no—
178#2618—611no—
179#2316—611no—
180#1519—612no—
181C2×#324D6111yescharacteristic, complemented
182#1289—612no—
183C2×C61—21no—
184C2×C61—21no—
185C2×C61—21no—
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61#187411yescharacteristic
190C2×C61#191211yescharacteristic
191C2×C61#191311yescharacteristic
192D61—161no—
193C2×#123—1221no—
194C2×#121—611no—
195C2×#117—1221no—
196C22×C4⋊C4C2×D6111yescharacteristic
197C2×C22⋊C8C2×D6112yes—
198#398—612no—
199#396—1222no—
200#394—612no—
201#389—1224no—
202#386—1221no—
203#380—611no—
204#380—612no—
205#380—1221no—
206#327—1224no—
207#324—22no—
208C61#920411yescharacteristic, complemented, Sylow
209C22×D4—611no—
210C22×D4—1221no—
211C23×C4D24411yescharacteristic
212C23×C4D24411yescharacteristic
213C23×C4C22×D6111yescharacteristic
214C22×C8—22no—
215#123—2442no—
216#123—2442no—
217#121—1222no—
218#121—1222no—
219#117—2442no—
220#117—2442no—
221C2×C4⋊C4—22no—
222C2×C4⋊C4—22no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—1222no—
225C2×C4⋊C4—1222no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1222no—
228C2×C4⋊C4—1222no—
229C2×C4⋊C4C4×D6112yes—
230C2×C4⋊C4C22⋊D6112yes—
231C2×C22⋊C4—1222no—
232C2×C22⋊C4—1222no—
233C2×C22⋊C4—1221no—
234C2×C22⋊C4—1222no—
235C2×C22⋊C4—1221no—
236C2×C42—1222no—
237C22⋊C8—22no—
238C22⋊C8—22no—
239#95—612no—
240#95—614no—
241#95—1222no—
242#95—1222no—
243C24—1221no—
244C24C2×D24411yescharacteristic
245C2×D4—1222no—
246C2×D4—4881no—
247C2×D4—2441no—
248C2×D4—2441no—
249C2×D4—2441no—
250C2×D4—2441no—
251C2×D4—2441no—
252C2×D4—2441no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—21no—
258C22×C4—21no—
259C22×C4—81no—
260C22×C4—81no—
261C22×C4—1222no—
262C22×C4—1221no—
263C22×C4—1224no—
264C22×C4#1175819012yes—
265C22×C4D48812yes—
266C22×C4#1175819812yes—
267C22×C4#1175819812yes—
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4D4×D6112yes—
270C22×C4#1175822412yes—
271C22×C4C2×C22⋊D6111yescharacteristic
272C2×C8—42no—
273C2×C8—82no—
274C4⋊C4—24no—
275C4⋊C4—24no—
276C4⋊C4—1222no—
277C4⋊C4—4882no—
278C4⋊C4—4881no—
279C4⋊C4—4882no—
280C4⋊C4—2444no—
281C4⋊C4—2444no—
282C22⋊C4—4882no—
283C22⋊C4—2442no—
284C22⋊C4—2441no—
285C22⋊C4—2441no—
286C22⋊C4—2442no—
287C22⋊C4—2444no—
288C22⋊C4—2442no—
289C42—2444no—
290C23—41no—
291C23—41no—
292C23—2442no—
293C23—2442no—
294C23—2441no—
295C23—2441no—
296C23—2441no—
297C23C2×#1175819811yescharacteristic
298C23#1451974711yescharacteristic
299C23#1451976111yescharacteristic
300C23C2×D48811yescharacteristic
301C23C2×#1175819011yescharacteristic
302C23#1451980511yescharacteristic
303C23#1451981011yescharacteristic
304D4—4882no—
305D4—4881no—
306D4—4881no—
307D4—4881no—
308D4—4881no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—22no—
313C2×C4—22no—
314C2×C4—22no—
315C2×C4—22no—
316C2×C4—42no—
317C2×C4—41no—
318C2×C4—42no—
319C2×C4—41no—
320C2×C4—42no—
321C2×C4—42no—
322C2×C4—81no—
323C2×C4—2442no—
324C2×C4—2444no—
325C2×C4—2444no—
326C2×C4—2442no—
327C2×C4—2442no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4—2444no—
332C2×C4#1451969914yes—
333C2×C4#1451973712yes—
334C2×C4#1451974912yes—
335C8—82no—
336C22—21no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—21no—
341C22—21no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—4882no—
347C22—4882no—
348C22—4881no—
349C22—4881no—
350C22—4881no—
351C22#1683963911yescharacteristic
352C22C2×#1451969911yescharacteristic
353C22#1683976411yescharacteristic
354C22#1683989811yescharacteristic
355C22#1683990311yescharacteristic
356C22#1684007611yescharacteristic
357C22#1684008111yescharacteristic
358C4—22no—
359C4—22no—
360C4—24no—
361C4—42no—
362C4—4884no—
363C4—4882no—
364C4—4881no—
365C2—21no—
366C2—21no—
367C2—21no—
368C2—21no—
369C2—21no—
370C2—21no—
371C2—9761no—
372C2#2144613411yescharacteristic
373C2#2144635411yescharacteristic
374C2#2144635911yescharacteristic
subgroupG/H
centerC22#16839639
commutatorC22×C4×C61C22×C4
FrattiniC23×C4C22×D61
FittingC2×C61×#324C2
socleC22×C61#386
prime radicalC2×#14519751C22
cosocleC23×C4×C61C23
hypercenterC2×#324D61
hypocenterC61#9204
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
2. #21448437C2semidirect
4. #21443687C2semidirect
5. C2×C61×#324C2semidirect
9. #16839692C4semidirect
11. #16839679C4semidirect
181. C2×#324D61semidirect
208. C61#9204semidirect

Maximal subgroups

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

subgroupindex
#214515612
#214484372
#214443882
#214436872
C2×C61×#3242
#920461