Finite Group Databasebeta

← #29568470

Subgroups — #29568470

Order 15616.

568 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21445513C211yesmaximal, characteristic
2C2×#16839517C211yesmaximal, characteristic
3#21443645C212yesmaximal, complemented
4#21443642C212yesmaximal, complemented
5C61×#2855C211yesmaximal, characteristic
6C22×#11758194—21no—
7C23×#92418—21no—
8#16839517—21no—
9#16839517—21no—
10#16839517C2212yes—
11#16839517C2212yes—
12C2×C22⋊Q8×C61C411yescharacteristic
13C22×C42×C61C2211yescharacteristic
14C61×#391C411yescharacteristic
15C61×#391C2211yescharacteristic
16C61×#389C411yescharacteristic
17C61×#389C2211yescharacteristic
18C61×#387—21no—
19C61×#387—21no—
20C61×#385—21no—
21C61×#381—21no—
22C61×#380C411yescharacteristic
23C2×#11758194—24no—
24C2×#11758194—42no—
25C2×#11758194—42no—
26C22×#92418—24no—
27C22×#92418—22no—
28C22×#92418—22no—
29C22×#92418—42no—
30C22×#92418—42no—
31C22×Q8×C61C2×C411yescharacteristic
32C23×C4×C61C2×C411yescharacteristic
33C23×C4×C61D411yescharacteristic
34C23×C4×C61D411yescharacteristic
35C22⋊Q8×C61—42no—
36C2×C4⋊C4×C61—21no—
37C2×C4⋊C4×C61—21no—
38C2×C4⋊C4×C61—21no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C2×C4⋊C4×C61C2×C411yescharacteristic
41C2×C4⋊C4×C61C2×C411yescharacteristic
42C2×C22⋊C4×C61—21no—
43C2×C22⋊C4×C61—21no—
44C2×C42×C61—42no—
45C2×C42×C61C2×C411yescharacteristic
46C2×C42×C61D411yescharacteristic
47C2×C42×C61D411yescharacteristic
48C2×C42×C61C2311yescharacteristic
49#95×C61—21no—
50#95×C61—21no—
51#95×C61—21no—
52#95×C61—21no—
53#95×C61—21no—
54#95×C61—21no—
55#95×C61—21no—
56C24×C61C22⋊C411yescharacteristic
57C2×Q8×C61—22no—
58C2×Q8×C61—41no—
59C2×Q8×C61—41no—
60C22×C4×C61—22no—
61C22×C4×C61—22no—
62C22×C4×C61—22no—
63C22×C4×C61—22no—
64C22×C4×C61—21no—
65C22×C4×C61—21no—
66C22×C4×C61—22no—
67C22×C4×C61—22no—
68C22×C4×C61—21no—
69C22×C4×C61—21no—
70C22×C4×C61—21no—
71C22×C4×C61—21no—
72C22×C4×C61—41no—
73C22×C4×C61C22⋊C411yescharacteristic
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61SD1612yes—
77C22×C4×C61Q1612yes—
78C22×C4×C61C22×C411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×C4×C61C2×D411yescharacteristic
81C4⋊C4×C61—22no—
82C4⋊C4×C61—42no—
83C4⋊C4×C61—41no—
84C4⋊C4×C61—41no—
85C4⋊C4×C61—42no—
86C4⋊C4×C61—41no—
87C4⋊C4×C61—41no—
88C22⋊C4×C61—42no—
89C22⋊C4×C61—42no—
90C42×C61—41no—
91C42×C61—41no—
92C42×C61—41no—
93C42×C61—41no—
94#11758194—48no—
95C2×#92418—24no—
96C2×#92418—24no—
97C2×#92418—48no—
98C2×#92418—42no—
99C2×#92418—42no—
100C2×#92418—42no—
101C2×#92418—42no—
102C23×C61—21no—
103C23×C61—21no—
104C23×C61—21no—
105C23×C61—21no—
106C23×C61#9912yes—
107C23×C61#10312yes—
108C23×C61#10412yes—
109C23×C61C2×C22⋊C411yescharacteristic
110Q8×C61—82no—
111C2×C4×C61—24no—
112C2×C4×C61—24no—
113C2×C4×C61—24no—
114C2×C4×C61—24no—
115C2×C4×C61—21no—
116C2×C4×C61—21no—
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—21no—
124C2×C4×C61—21no—
125C2×C4×C61—21no—
126C2×C4×C61—21no—
127C2×C4×C61—21no—
128C2×C4×C61—44no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61—41no—
132C2×C4×C61—41no—
133C2×C4×C61—41no—
134C2×C4×C61—41no—
135C2×C4×C61—41no—
136C2×C4×C61—41no—
137C2×C4×C61—41no—
138C2×C4×C61—41no—
139C2×C4×C61—41no—
140C2×C4×C61—41no—
141C2×C4×C61#10312yes—
142C2×C4×C61#10412yes—
143C2×C4×C61#13112yes—
144C2×C4×C61C2×SD1611yescharacteristic
145C2×C4×C61C2×Q1611yescharacteristic
146C2×C4×C61AGL(1,ℤ/8)11yescharacteristic
147C2×C4×C61#13711yescharacteristic
148#92418—44no—
149#92418—44no—
150#7681—611nomaximal, Sylow
151C22×C61—22no—
152C22×C61—22no—
153C22×C61—22no—
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61#32814yes—
158C22×C61#40811yescharacteristic
159C22×C61C2×#9911yescharacteristic
160C22×C61#41311yescharacteristic
161C22×C61C2×#10311yescharacteristic
162C22×C61#41711yescharacteristic
163C22×C61C2×#10411yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C4×C61—22no—
166C4×C61—21no—
167C4×C61—22no—
168C4×C61—21no—
169C4×C61—21no—
170C4×C61—22no—
171C4×C61—21no—
172C4×C61—41no—
173C4×C61—81no—
174C4×C61—81no—
175C4×C61—81no—
176C4×C61—81no—
177#2855D6111yescharacteristic
178#1728—611no—
179C2×#336—611no—
180#1272—612no—
181#1271—612no—
182C2×C61—24no—
183C2×C61#146811yescharacteristic
184C2×C61#148311yescharacteristic
185C2×C61#149311yescharacteristic
186C2×C61C2×#32811yescharacteristic
187C2×C61#150411yescharacteristic
188C2×C61#152411yescharacteristic
189C2×C61#155011yescharacteristic
190C22×M16—1221no—
191C23×C8—1221no—
192C2×C22⋊Q8Dic6111yescharacteristic
193C22×C42C2×D6111yescharacteristic
194#391Dic6111yescharacteristic
195#391C2×D6111yescharacteristic
196#389Dic6111yescharacteristic
197#389C2×D6111yescharacteristic
198#387—21no—
199#387—21no—
200#385—21no—
201#381—21no—
202#380Dic6111yescharacteristic
203#336—612no—
204#336—612no—
205#336—1221no—
206#336—1221no—
207C61#768111yescharacteristic, complemented, Sylow
208C22×Q8C2×Dic6111yescharacteristic
209C23×C4C2×Dic6111yescharacteristic
210C23×C4C22⋊D6111yescharacteristic
211C23×C4C22⋊D6111yescharacteristic
212C2×M16—1224no—
213C2×M16—2442no—
214C2×M16—2442no—
215C22×C8—1224no—
216C22×C8—1222no—
217C22×C8—1222no—
218C22×C8—2442no—
219C22×C8—2442no—
220C22⋊Q8—42no—
221C2×C4⋊C4—21no—
222C2×C4⋊C4—21no—
223C2×C4⋊C4—21no—
224C2×C4⋊C4C2×Dic6111yescharacteristic
225C2×C4⋊C4C2×Dic6111yescharacteristic
226C2×C4⋊C4C2×Dic6111yescharacteristic
227C2×C22⋊C4—21no—
228C2×C22⋊C4—21no—
229C2×C42—42no—
230C2×C42C2×Dic6111yescharacteristic
231C2×C42C22⋊D6111yescharacteristic
232C2×C42C22⋊D6111yescharacteristic
233C2×C42C22×D6111yescharacteristic
234#95—21no—
235#95—21no—
236#95—21no—
237#95—21no—
238#95—21no—
239#95—21no—
240#95—21no—
241C24C22⋊Dic6111yescharacteristic
242C2×Q8—22no—
243C2×Q8—41no—
244C2×Q8—41no—
245C22×C4—22no—
246C22×C4—22no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—21no—
250C22×C4—21no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—21no—
256C22×C4—21no—
257C22×C4—41no—
258C22×C4#1175820112yes—
259C22×C4#1175820212yes—
260C22×C4C22⋊Dic6111yescharacteristic
261C22×C4C22⋊Dic6111yescharacteristic
262C22×C4C22⋊Dic6111yescharacteristic
263C22×C4C22×Dic6111yescharacteristic
264C22×C4C2×C22⋊D6111yescharacteristic
265C22×C4C2×C22⋊D6111yescharacteristic
266M16—2448no—
267C2×C8—1224no—
268C2×C8—1224no—
269C2×C8—2448no—
270C2×C8—2442no—
271C2×C8—2442no—
272C2×C8—2442no—
273C2×C8—2442no—
274C4⋊C4—22no—
275C4⋊C4—41no—
276C4⋊C4—41no—
277C4⋊C4—42no—
278C4⋊C4—42no—
279C4⋊C4—41no—
280C4⋊C4—41no—
281C22⋊C4—42no—
282C22⋊C4—42no—
283C42—41no—
284C42—41no—
285C42—41no—
286C42—41no—
287C23—21no—
288C23—21no—
289C23—21no—
290C23—21no—
291C23#1451969212yes—
292C23#1451970112yes—
293C23#1451970412yes—
294C23C2×C22⋊Dic6111yescharacteristic
295Q8—82no—
296C2×C4—24no—
297C2×C4—24no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—44no—
314C2×C4—41no—
315C2×C4—41no—
316C2×C4—41no—
317C2×C4—41no—
318C2×C4—41no—
319C2×C4—41no—
320C2×C4—41no—
321C2×C4—41no—
322C2×C4—41no—
323C2×C4—41no—
324C2×C4—41no—
325C2×C4—41no—
326C2×C4#1451970112yes—
327C2×C4#1451970412yes—
328C2×C4#1451978412yes—
329C2×C4C2×#1175820111yescharacteristic
330C2×C4C2×#1175820211yescharacteristic
331C2×C4#1451980211yescharacteristic
332C2×C4#1451980711yescharacteristic
333C8—2444no—
334C8—2444no—
335C22—22no—
336C22—22no—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22#1683949914yes—
342C22#1683972911yescharacteristic
343C22C2×#1451969211yescharacteristic
344C22#1683974611yescharacteristic
345C22C2×#1451970111yescharacteristic
346C22#1683976311yescharacteristic
347C22C2×#1451970411yescharacteristic
348C22C2×#1451970411yescharacteristic
349C4—22no—
350C4—21no—
351C4—22no—
352C4—21no—
353C4—21no—
354C4—22no—
355C4—21no—
356C4—41no—
357C4—81no—
358C4—81no—
359C4—81no—
360C4—81no—
361C2—24no—
362C2#2144416711yescharacteristic
363C2#2144423211yescharacteristic
364C2#2144427411yescharacteristic
365C2C2×#1683949911yescharacteristic
366C2#2144432311yescharacteristic
367C2#2144440711yescharacteristic
368C2#2144450911yescharacteristic
subgroupG/H
centerC23C2×C22⋊Dic61
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#2855C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#2855D61
hypocenterC61#7681
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #2855

Complements

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

NH ≅ G/Ntype
3. #21443645C2semidirect
4. #21443642C2semidirect
207. C61#7681semidirect

Maximal subgroups

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

subgroupindex
#214455132
C2×#168395172
#214436452
#214436422
C61×#28552
#768161