Finite Group Databasebeta

← #29575621

Subgroups — #29575621

Order 15616.

614 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#11758194C211yesmaximal, characteristic
2#21454129C211yesmaximal, characteristic
3C2×#16839503C212yesmaximal, complemented
4#21443701C212yesmaximal, complemented
5C61×#1749C211yesmaximal, characteristic
6C22×#11758194—21no—
7C2×#14519769C2211yescharacteristic
8C4×#11758194—24no—
9C2×#14519688C2212yes—
10C2×C4×#92418—21no—
11#16839660C411yescharacteristic
12#16839660C411yescharacteristic
13#16839646—21no—
14#16839646—21no—
15#16839635—21no—
16#16839635—21no—
17#16839628C2211yescharacteristic
18#16839622C411yescharacteristic
19#16839622C411yescharacteristic
20#16839503—24no—
21C22×C42×C61C2211yescharacteristic
22C2×C22⋊C8×C61—21no—
23C2×#97×C61C2212yes—
24C61×#336—21no—
25C2×#11758194—24no—
26C2×#11758194—24no—
27C2×#11758194—24no—
28C22×#92418—22no—
29#14519769—22no—
30#14519769—22no—
31C2×C4⋊Dic61C2×C411yescharacteristic
32C2×C4⋊Dic61C2×C411yescharacteristic
33C2×C4⋊Dic61C2×C411yescharacteristic
34C2×C4⋊Dic61C2×C411yescharacteristic
35C2×#11758196—21no—
36C2×#11758196—21no—
37C2×#11758196—21no—
38C2×#11758196—21no—
39C2×C22⋊Dic61—21no—
40C2×C22⋊Dic61—21no—
41#14519688—22no—
42#14519688D414yes—
43C4×#92418—24no—
44#14519684—21no—
45#14519684—21no—
46#14519684—21no—
47#14519684—21no—
48#14519684—21no—
49#14519684—21no—
50C23×C4×C61C2×C411yescharacteristic
51C23×C4×C61D411yescharacteristic
52C23×C4×C61D411yescharacteristic
53C22×C8×C61—22no—
54C2×C42×C61—22no—
55C2×C42×C61—22no—
56C2×C42×C61C2×C411yescharacteristic
57C2×C42×C61D411yescharacteristic
58C2×C42×C61D411yescharacteristic
59C2×C42×C61C2311yescharacteristic
60C22⋊C8×C61—24no—
61#97×C61—22no—
62#97×C61—22no—
63C24×C61C22⋊C411yescharacteristic
64C22×C4×C61—22no—
65C22×C4×C61—22no—
66C22×C4×C61—21no—
67C22×C4×C61—21no—
68C22×C4×C61—22no—
69C22×C4×C61—22no—
70C22×C4×C61—22no—
71C22×C4×C61—22no—
72C22×C4×C61—41no—
73C22×C4×C61—41no—
74C22×C4×C61C22⋊C411yescharacteristic
75C22×C4×C61C22⋊C411yescharacteristic
76C22×C4×C61C22⋊C411yescharacteristic
77C22×C4×C61C22×C411yescharacteristic
78C22×C4×C61C2×D411yescharacteristic
79C22×C4×C61C2×D411yescharacteristic
80C22×Dic61—21no—
81C22×Dic61—21no—
82C22×Dic61—21no—
83C22×Dic61—21no—
84C2×C8×C61—24no—
85C2×C8×C61—42no—
86C2×C8×C61—42no—
87C42×C61—22no—
88C42×C61—21no—
89C42×C61—22no—
90C42×C61—21no—
91C42×C61C2×D412yes—
92C42×C61#4112yes—
93C22⋊Dic61—42no—
94C22⋊Dic61—42no—
95C4⋊Dic61—22no—
96C4⋊Dic61—22no—
97C4⋊Dic61—41no—
98C4⋊Dic61—41no—
99#11758196—42no—
100#11758196—42no—
101#11758196—41no—
102#11758196—42no—
103#11758196—41no—
104#11758194—216no—
105C2×#92418—24no—
106C2×#92418—24no—
107C2×#92418—24no—
108C23×C61—21no—
109C23×C61—21no—
110C23×C61—21no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61#10412yes—
115C23×C61C2×C22⋊C411yescharacteristic
116C2×C4×C61—24no—
117C2×C4×C61—24no—
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—21no—
129C2×C4×C61—21no—
130C2×C4×C61—44no—
131C2×C4×C61—44no—
132C2×C4×C61#10112yes—
133C2×C4×C61#10412yes—
134C2×C4×C61#10412yes—
135C2×C4×C61C4×D412yes—
136C2×C4×C61#12011yescharacteristic
137C2×C4×C61#12112yes—
138C2×C4×C61#12311yescharacteristic
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—41no—
150C2×Dic61—41no—
151C8×C61—44no—
152#92418—28no—
153#9122—611nomaximal, Sylow
154C22×C61—22no—
155C22×C61—22no—
156C22×C61—22no—
157C22×C61—41no—
158C22×C61—41no—
159C22×C61—41no—
160C22×C61—41no—
161C22×C61#38611yescharacteristic
162C22×C61C2×#10111yescharacteristic
163C22×C61#41311yescharacteristic
164C22×C61C2×#10411yescharacteristic
165C22×C61C2×#10411yescharacteristic
166C22×C61C2×#10411yescharacteristic
167C22×C61#42111yescharacteristic
168C4×C61—22no—
169C4×C61—22no—
170C4×C61—21no—
171C4×C61—22no—
172C4×C61—21no—
173C4×C61—22no—
174C4×C61—22no—
175Dic61—81no—
176Dic61—81no—
177Dic61—81no—
178Dic61—81no—
179C2×C4×M16—611no—
180#2851—611no—
181#1749D6111yescharacteristic
182C2×#330—612no—
183#1295—612no—
184C2×C61—42no—
185C2×C61#152411yescharacteristic
186C2×C61#152611yescharacteristic
187C2×C61#152811yescharacteristic
188C2×C61#152911yescharacteristic
189C2×C61#187111yescharacteristic
190C2×C61#189611yescharacteristic
191C2×C61#190111yescharacteristic
192C22×M16—1221no—
193C2×#125—611no—
194C22×C42C2×D6111yescharacteristic
195C2×C22⋊C8—21no—
196C4×M16—1224no—
197C2×#97—612no—
198C2×#97C2×D6112yes—
199C2×C4×C8—1221no—
200#389—611no—
201#389—611no—
202#387—1221no—
203#387—1221no—
204#385—1221no—
205#385—1221no—
206#382—611no—
207#380—611no—
208#380—611no—
209#336—21no—
210#330—1224no—
211C61#912211yescharacteristic, complemented, Sylow
212C23×C4C4×D6111yescharacteristic
213C23×C4D24411yescharacteristic
214C23×C4C22⋊D6111yescharacteristic
215C2×M16—1224no—
216C2×M16—1224no—
217C2×M16—1224no—
218C22×C8—22no—
219C22×C8—1222no—
220#125—1222no—
221#125—1222no—
222C2×C4⋊C4—611no—
223C2×C4⋊C4—611no—
224C2×C4⋊C4—611no—
225C2×C4⋊C4—611no—
226C2×C4⋊C4—1221no—
227C2×C4⋊C4—1221no—
228C2×C4⋊C4—1221no—
229C2×C4⋊C4—1221no—
230C2×C22⋊C4—1221no—
231C2×C22⋊C4—1221no—
232C2×C42—22no—
233C2×C42—22no—
234C2×C42C4×D6111yescharacteristic
235C2×C42D24411yescharacteristic
236C2×C42C22⋊D6111yescharacteristic
237C2×C42C22×D6111yescharacteristic
238C22⋊C8—24no—
239#97—22no—
240#97—22no—
241#97—614no—
242#97—1222no—
243C4×C8—1224no—
244#95—1221no—
245#95—1221no—
246#95—1221no—
247#95—1221no—
248#95—1221no—
249#95—1221no—
250C24#1175819811yescharacteristic
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—22no—
256C22×C4—22no—
257C22×C4—22no—
258C22×C4—22no—
259C22×C4—41no—
260C22×C4—41no—
261C22×C4—1221no—
262C22×C4—1221no—
263C22×C4—1221no—
264C22×C4—1221no—
265C22×C4#1175819811yescharacteristic
266C22×C4#1175819811yescharacteristic
267C22×C4#1175819811yescharacteristic
268C22×C4C2×C4×D6111yescharacteristic
269C22×C4C2×D24411yescharacteristic
270C22×C4C2×C22⋊D6111yescharacteristic
271M16—12216no—
272C2×C8—24no—
273C2×C8—42no—
274C2×C8—42no—
275C2×C8—1224no—
276C2×C8—1224no—
277C2×C8—1224no—
278C4⋊C4—1222no—
279C4⋊C4—1222no—
280C4⋊C4—2441no—
281C4⋊C4—2441no—
282C4⋊C4—2442no—
283C4⋊C4—2442no—
284C4⋊C4—2441no—
285C4⋊C4—2442no—
286C4⋊C4—2441no—
287C22⋊C4—2442no—
288C22⋊C4—2442no—
289C42—22no—
290C42—21no—
291C42—22no—
292C42—21no—
293C42D4×D6112yes—
294C42#1175822412yes—
295C23—21no—
296C23—21no—
297C23—21no—
298C23—21no—
299C23—21no—
300C23—21no—
301C23#1451970312yes—
302C23C2×#1175819811yescharacteristic
303C2×C4—24no—
304C2×C4—24no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—21no—
314C2×C4—21no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—2441no—
320C2×C4—2441no—
321C2×C4—2441no—
322C2×C4—2441no—
323C2×C4—2441no—
324C2×C4—2441no—
325C2×C4—2441no—
326C2×C4—2441no—
327C2×C4—2441no—
328C2×C4—2441no—
329C2×C4—2441no—
330C2×C4—2441no—
331C2×C4#1451969512yes—
332C2×C4#1451970312yes—
333C2×C4#1451970512yes—
334C2×C4#1451973712yes—
335C2×C4#1451974711yescharacteristic
336C2×C4#1451974912yes—
337C2×C4#1451976111yescharacteristic
338C8—44no—
339C8—1228no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22#1683963911yescharacteristic
348C22C2×#1451969511yescharacteristic
349C22#1683974411yescharacteristic
350C22C2×#1451970311yescharacteristic
351C22C2×#1451970311yescharacteristic
352C22C2×#1451970511yescharacteristic
353C22#1683978011yescharacteristic
354C4—21no—
355C4—22no—
356C4—21no—
357C4—22no—
358C4—22no—
359C4—22no—
360C4—22no—
361C4—4881no—
362C4—4881no—
363C4—4881no—
364C4—4881no—
365C2—42no—
366C2#2144440511yescharacteristic
367C2#2144441311yescharacteristic
368C2#2144442211yescharacteristic
369C2#2144442711yescharacteristic
370C2#2144611911yescharacteristic
371C2#2144626011yescharacteristic
372C2#2144628511yescharacteristic
subgroupG/H
centerC23C2×#11758198
commutatorC22×C4×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1749C2
socleC23×C61C2×C22⋊C4
prime radicalC24×C61C22⋊C4
cosocleC2×C42×C61C23
hypercenter#1749D61
hypocenterC61#9122
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C22×C42 ◁ #1749

Complements

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

NH ≅ G/Ntype
3. C2×#16839503C2semidirect
4. #21443701C2semidirect
211. C61#9122semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#117581942
#214541292
C2×#168395032
#214437012
C61×#17492
#912261